The emphasis of this postcard is obviously the City Hall, not the streetcar, but if you look off to the left there it is. Another thing I noticed about this card is that the people who tinted the German and Dutch cards tended to make small but very stylized and distinctive clouds. The American ones often have a bank of clouds. Do you care? Probably not, but if you look at enough postcards you start to notice these things.
The streetcar system in Leipzig, Germany developed in a similar fashion to other systems around the world. The Leipzig trams, or streetcars, started out in 1872 as horse-drawn cars, with service provided by the Leipziger Pferdeeisenbahn (Leipzig Horse railway.) The company was enormously successful and eventually owned 1,013 horses and 172 cars. Life was good until the competition came along.
That's another commonality with other systems around the world. Today, public transit is typically provided by a jurisdiction or by a single entity. There is rarely competition or duplication between systems. But in the early days of the streetcar, there were often multiple service providers, even in small towns. This in turn led to some systems going under and also consolidations. In the case of Leipzig, the new competitor came along in the 1800s and started developing an electric tramway system. This action spurred the horse-car railway folks to convert to electric power too. The last horse-drawn car service operated in 1897.
After World War I, the systems were replaced by a publicly-operated system, which eventually also operated buses and trolleybuses. Many streetcar segments were damaged or closed for other reasons during World War II. The closures continued after the war, although the antiquated streetcar system operated continuously. A real resurgence in streetcar development in Leipzig didn't take place until the 1980s, when a number of new segments were opened. You can see a detailed history of the Leipzig streetcar system here. You can also visit this site to see what the current system looks like.